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Energy games, which model quantitative consumption of a limited resource, e.g., time or energy, play a central role in quantitative models for reactive systems. Reactive synthesis constructs a controller which satisfies a given…
Matthew Baker investigated, in previous work, an elegant, infinite-length game that may be used to study subsets of real numbers. We present two accessible examples of how an important technique from set theory, or a different technique…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
We study turn-based quantitative games of infinite duration opposing two antagonistic players and played over graphs. This model is widely accepted as providing the adequate framework for formalizing the synthesis question for reactive…
We consider a class of infinite-state stochastic games generated by stateless pushdown automata (or, equivalently, 1-exit recursive state machines), where the winning objective is specified by a regular set of target configurations and a…
We provide a learning-based technique for guessing a winning strategy in a parity game originating from an LTL synthesis problem. A cheaply obtained guess can be useful in several applications. Not only can the guessed strategy be applied…
Parity games can be used to represent many different kinds of decision problems. In practice, tools that use parity games often rely on a specification in a higher-order logic from which the actual game can be obtained by means of an…
In this paper, some new criteria for detecting whether a finite game is potential are proposed by solving potential equations. The verification equations with the minimal number for checking a potential game are obtained for the first time.…
We study two-player zero-sum games over infinite-state graphs with boundedness conditions. Our first contribution is about the strategy complexity, i.e the memory required for winning strategies: we prove that over general infinite-state…
We present a systematic investigation of the quantum games, constructed using a novel repeated game protocol, when played repeatedly ad infinitum. We focus on establishing that such repeated games -- by virtue of inherent quantum-mechanical…
We prove game-theoretic versions of several classical results on nonrepetitive sequences, showing the existence of winning strategies using an extension of the Lov\'asz Local Lemma which can dramatically reduce the number of edges needed in…
Autonomous agents should coordinate effectively without prior knowledge of others' intents. While prior work has focused on intent inference, we address the inverse problem: how agents can strategically demonstrate their intents within…
The performance of two pivoting algorithms, due to Lemke and Cottle and Dantzig, is studied on linear complementarity problems (LCPs) that arise from infinite games, such as parity, average-reward, and discounted games. The algorithms have…
We consider ways to construct a transducer for a given set of input word to output symbol pairs. This is motivated by the need for representing game playing programs in a low-level mathematical format that can be analyzed by algebraic…
Imitation is simple behavior which uses successful actions of others in order to deal with one's own problems. Because success of imitation generally depends on whether profit of an imitating agent coincides with those of other agents or…
Inductions and game semantics are two useful extensions to traditional logic programming. To be specific, inductions can capture a wider class of provable formulas in logic programming. Adopting game semantics can make logic programming…
We study two-player zero-sum concurrent stochastic games with finite state and action space played for an infinite number of steps. In every step, the two players simultaneously and independently choose an action. Given the current state…
In this invited contribution, we propose a comprehensive introduction to game theory applied in computer aided synthesis. In this context, we give some classical results on two-player zero-sum games and then on multi-player non zero-sum…
The computation of a solution concept of a cooperative game usually employs values of all coalitions. However, in some applications, the values of some of the coalitions might be unknown due to high costs associated with their determination…
We present a functional framework for automated mechanism design based on a two-stage game model of strategic interaction between the designer and the mechanism participants, and apply it to several classes of two-player infinite games of…